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Centroid (Function)

By analogy with the Geometric Centroid, the centroid of an arbitrary function $f(x)$ is defined as

\begin{displaymath}
\left\langle{x}\right\rangle{}={\int_{-\infty}^\infty xf(x)\,dx\over\int_{-\infty}^\infty f(x)\,dx}.
\end{displaymath}


References

Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 139-140 and 156, 1965.




© 1996-9 Eric W. Weisstein
1999-05-26